#define BLACK 1
#define RED 0
#include <iostream>

using namespace std;

class bst {
private:

    struct Node {
        int value;
        bool color;
        Node *leftTree, *rightTree, *parent;

        Node() : value(0), color(RED), leftTree(NULL), rightTree(NULL), parent(NULL) { }        

        Node* grandparent() {
            if(parent == NULL){
                return NULL;
            }
            return parent->parent;
        }

        Node* uncle() {
            if(grandparent() == NULL) {
                return NULL;
            }
            if(parent == grandparent()->rightTree)
                return grandparent()->leftTree;
            else
                return grandparent()->rightTree;
        }

        Node* sibling() {
            if(parent->leftTree == this)
                return parent->rightTree;
            else
                return parent->leftTree;
        }
    };

    void rotate_right(Node *p){
        Node *gp = p->grandparent();
        Node *fa = p->parent;
        Node *y = p->rightTree;

        fa->leftTree = y;

        if(y != NIL)
            y->parent = fa;
        p->rightTree = fa;
        fa->parent = p;

        if(root == fa)
            root = p;
        p->parent = gp;

        if(gp != NULL){
            if(gp->leftTree == fa)
                gp->leftTree = p;
            else
                gp->rightTree = p;
        }

    }

    void rotate_left(Node *p){
        if(p->parent == NULL){
            root = p;
            return;
        }
        Node *gp = p->grandparent();
        Node *fa = p->parent;
        Node *y = p->leftTree;

        fa->rightTree = y;

        if(y != NIL)
            y->parent = fa;
        p->leftTree = fa;
        fa->parent = p;

        if(root == fa)
            root = p;
        p->parent = gp;

        if(gp != NULL){
            if(gp->leftTree == fa)
                gp->leftTree = p;
            else
                gp->rightTree = p;
        }
    }

    void inorder(Node *p){
        if(p == NIL)
            return;

        if(p->leftTree)
            inorder(p->leftTree);

        cout << p->value << " ";
                
        if(p->rightTree)
            inorder(p->rightTree);
    }

    string outputColor (bool color) {
        return color ? "BLACK" : "RED";
    }

    Node* getSmallestChild(Node *p){
        if(p->leftTree == NIL)
            return p;
        return getSmallestChild(p->leftTree);
    }

    bool delete_child(Node *p, int data){
        if(p->value > data){
            if(p->leftTree == NIL){
                return false;
            }
            return delete_child(p->leftTree, data);
        } else if(p->value < data){
            if(p->rightTree == NIL){
                return false;
            }
            return delete_child(p->rightTree, data);
        } else if(p->value == data){
            if(p->rightTree == NIL){
                delete_one_child (p);
                return true;
            }
            Node *smallest = getSmallestChild(p->rightTree);
            swap(p->value, smallest->value);
            delete_one_child (smallest);

            return true;
        }else{
           return false;
         }
    }

    void delete_one_child(Node *p){
        Node *child = p->leftTree == NIL ? p->rightTree : p->leftTree;
        if(p->parent == NULL && p->leftTree == NIL && p->rightTree == NIL){
            p = NULL;
            root = p;
            return;
        }
        
        if(p->parent == NULL){
            delete  p;
            child->parent = NULL;
            root = child;
            root->color = BLACK;
            return;
        }
        
        if(p->parent->leftTree == p){
            p->parent->leftTree = child;
        } else {
            p->parent->rightTree = child;
        }
        child->parent = p->parent;

        if(p->color == BLACK){
            if(child->color == RED){
                child->color = BLACK;
            } else
                delete_case (child);
        }

        delete p;
    }

    void delete_case(Node *p){
        if(p->parent == NULL){
            p->color = BLACK;
            return;
        }
        if(p->sibling()->color == RED) {
            p->parent->color = RED;
            p->sibling()->color = BLACK;
            if(p == p->parent->leftTree)
                rotate_left(p->sibling());
            else
                rotate_right(p->sibling());
        }
        if(p->parent->color == BLACK && p->sibling()->color == BLACK
                && p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
            p->sibling()->color = RED;
            delete_case(p->parent);
        } else if(p->parent->color == RED && p->sibling()->color == BLACK
                && p->sibling()->leftTree->color == BLACK && p->sibling()->rightTree->color == BLACK) {
            p->sibling()->color = RED;
            p->parent->color = BLACK;
        } else {
            if(p->sibling()->color == BLACK) {
                if(p == p->parent->leftTree && p->sibling()->leftTree->color == RED
                        && p->sibling()->rightTree->color == BLACK) {
                    p->sibling()->color = RED;
                    p->sibling()->leftTree->color = BLACK;
                    rotate_right(p->sibling()->leftTree);
                } else if(p == p->parent->rightTree && p->sibling()->leftTree->color == BLACK
                        && p->sibling()->rightTree->color == RED) {
                    p->sibling()->color = RED;
                    p->sibling()->rightTree->color = BLACK;
                    rotate_left(p->sibling()->rightTree);
                }
            }
            p->sibling()->color = p->parent->color;
            p->parent->color = BLACK;
            if(p == p->parent->leftTree){
                p->sibling()->rightTree->color = BLACK;
                rotate_left(p->sibling());
            } else {
                p->sibling()->leftTree->color = BLACK;
                rotate_right(p->sibling());
            }
        }
    }

    void insert(Node *p, int data){
        if(p->value >= data){
            if(p->leftTree != NIL)
                insert(p->leftTree, data);
            else {
                Node *tmp = new Node();
                tmp->value = data;
                tmp->leftTree = tmp->rightTree = NIL;
                tmp->parent = p;
                p->leftTree = tmp;
                insert_case (tmp);
            }
        } else {
            if(p->rightTree != NIL)
                insert(p->rightTree, data);
            else {
                Node *tmp = new Node();
                tmp->value = data;
                tmp->leftTree = tmp->rightTree = NIL;
                tmp->parent = p;
                p->rightTree = tmp;
                insert_case (tmp);
            }
        }
    }

    void insert_case(Node *p){
        if(p->parent == NULL){
            root = p;
            p->color = BLACK;
            return;
        }
        if(p->parent->color == RED){
            if(p->uncle()->color == RED) {
                p->parent->color = p->uncle()->color = BLACK;
                p->grandparent()->color = RED;
                insert_case(p->grandparent());
            } else {
                if(p->parent->rightTree == p && p->grandparent()->leftTree == p->parent) {
                    rotate_left (p);
                    rotate_right (p);
                    p->color = BLACK;
                    p->leftTree->color = p->rightTree->color = RED;
                } else if(p->parent->leftTree == p && p->grandparent()->rightTree == p->parent) {
                    rotate_right (p);
                    rotate_left (p);
                    p->color = BLACK;
                    p->leftTree->color = p->rightTree->color = RED;
                } else if(p->parent->leftTree == p && p->grandparent()->leftTree == p->parent) {
                    p->parent->color = BLACK;
                    p->grandparent()->color = RED;
                    rotate_right(p->parent);
                } else if(p->parent->rightTree == p && p->grandparent()->rightTree == p->parent) {
                    p->parent->color = BLACK;
                    p->grandparent()->color = RED;
                    rotate_left(p->parent);
                }
            }
        }
    }

    void DeleteTree(Node *p){
        if(!p || p == NIL){
            return;
        }
        DeleteTree(p->leftTree);
        DeleteTree(p->rightTree);
        delete p;
    }
public:

    bst() {
        NIL = new Node();
        NIL->color = BLACK;
        root = NULL;
    }

    ~bst() {
        if (root)
            DeleteTree (root);
        delete NIL;
    }

    void inorder() {
        if(root == NULL)
            return;
        inorder (root);
        cout << endl;
    }

    void insert (int x) {
        if(root == NULL){
            root = new Node();
            root->color = BLACK;
            root->leftTree = root->rightTree = NIL;
            root->value = x;
        } else {
            insert(root, x);
        }
    }

    bool delete_value (int data) {
        return delete_child(root, data);
    }
private:
    Node *root, *NIL;
};